document.write( "Question 1201844: (z+1)^4=1-i \n" ); document.write( "

Algebra.Com's Answer #836386 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Use deMoivre's Theorem.

\n" ); document.write( " $\"%28z%2B1%29%5E4=1-i=sqrt%282%29%2Acis%287pi%2F4%29=%282%5E%281%2F2%29%29%2Acis%287pi%2F4%29\"$

\n" ); document.write( "The \"primary\" 4th root of that expression is

\n" ); document.write( " $\"z%2B1=%282%5E%281%2F8%29%29%2Acis%287pi%2F16%29\"$

\n" ); document.write( "The other 4th roots of the expression have the same magnitude and are spaced around the Argand plane at intervals of (2pi)/4 = pi/2 radians:

\n" ); document.write( " $\"z%2B1=%282%5E%281%2F8%29%29%2Acis%2815pi%2F16%29\"$
\n" ); document.write( " $\"z%2B1=%282%5E%281%2F8%29%29%2Acis%2823pi%2F16%29\"$
\n" ); document.write( " $\"z%2B1=%282%5E%281%2F8%29%29%2Acis%2831pi%2F16%29\"$

\n" ); document.write( "Subtract 1 from each of those expressions to find the values of z....

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